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Chapter 5: Q22 (page 170)

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 65 and 20 respectively.

Step by step solution

01

Step 1. Description of step.

The sum of measures of all the angles of a triangle is 180.

Consider ΔAOD, such that,

m∠AOD+m∠ADO+m∠DAO=180m∠AOD+x−y+x+y=180m∠AOD+2x=180m∠AOD=180−2x

02

Step 2. Description of step.

From the given figure,

m∠AOD+m∠DOC=180m∠AOD+130=180m∠AOD=50°

03

Step 3. Description of step.

Substitute 50 for m∠AODinto m∠AOD=180−2x to find the value of x.

50=180−2x2x=180−502x=130x=65

04

Step 4. Alternate interior angles.

From the figure, it can be observed that, AD¯∥BC¯, AC¯is a transversal and ∠DAC,∠ACBare alternate interior angles such that

m∠DAC=m∠ACBx+y=85

05

Step 5. Description of step.

Substitute 65 for x into x+y=85 to find the value of y.

65+y=85y=85−65=20

Therefore, the value of x and y is 65 and 20 respectively.

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Most popular questions from this chapter

For the following figure, if WR¯⊥CE¯then name all angles congruent to ∠RCE.

The coordinates of the three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.

(-1,0),(2,-2),(2,2)

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SO=12SC;KO=12KA

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD; W, X, Y, Z are midpoints of AO¯, BO¯, CO¯and DO¯.

Prove: role="math" localid="1637745814874" WXYZ is a parallelogram.
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